1. Field of the Invention
This invention relates to optical systems in general and, in particular, to optical systems having reflecting elements containing multi-layer coatings on the reflecting surface.
2. Summary of the Prior Art
The use of multi-layer coatings to increase the reflectance of the front of an optical surface, for example a mirror, is well known in the art. Multi-layer reflection coatings are applied by alternately depositing layers of material, such as silicon dioxide and titanium dioxide, in alternating layers in thicknesses calculated by methods well known to those skilled in the art, to increase the reflectance of a reflecting surface at desired wavelengths. Many known techniques are available for depositing the multi-layer coatings. For example, they may be deposited in a coating chamber by sputtering or by electron beam deposition. It is also known that thickness variations in the coating across the surface of an optical element will cause wavefront errors in the optical beam reflected from the reflecting surface. It is well known and is a common problem in the field of depositing coatings that the uniform deposition of a multi-layer coating is difficult to achieve on a large optical component such as a reflecting mirror, due to the physical constraints of the coating chambers utilized for depositing optical coatings. In particular, it is often difficult to provide adequate spacing between the source of the material to be deposited and the surface to be coated to avoid the non-uniform deposition of material onto the surface to be coated. Frequently, the deposited coatings will be reasonably uniform in thickness in the center of the optical element but will gradually taper off by as much as twenty-five percent (25%) at the edge of a large optical element. While various techniques, such as rotation of the optical element to be coated and the use of masks, can be used to reduce the non-uniformity, it is difficult to entirely eliminate the wavefront error due to the variation in thickness of the deposited coating.
It is known that light that is reflected from a multi-layered dielectric coating experiences a phase shift that depends on the wavelength of the reflected light and the types and thicknesses of material forming the reflection coating. These effects combine to give a net phase shift on reflection. If the coating on the mirror's surface is non-uniform in thickness, the phase shift in one region of the mirror, for example at the location where the coating is thin, will not match the phase shift elsewhere, thereby causing a wavefront error in the reflected beam. The amount of the wavefront error is given approximately by the equation: ##EQU1##
The first term is due to the undulation of the top surface of the coating while the second term (i.e. .DELTA..phi.) is due to the variation of thickness of the coating layers. In practice, the first term is usually much larger than the second term.
The wavefront error has only been a minor problem for most optical components, and thus this problem has received little study. Prior to this time the only technique used to reduce the wavefront error has been to reduce the thickness variation. This invention has been developed to reduce the wavefront error even though a thickness variation is present.